Journal of Symplectic Geometry

Volume 9 (2011)

Number 2

Tamed to compatible: symplectic forms via moduli space integration

Pages: 161 – 250



Clifford Henry Taubes


Fix a compact 4-dimensional manifold with self-dual second Betti number one and with a given symplectic form. This article proves the following: The Frêchet space of tamed almost complex structures as defined by the given symplectic form has an open and dense subset whose complex structures are compatible with respect to a symplectic form that is cohomologous to the given one. The theorem is proved by constructing the new symplectic form by integrating over a space of currents that are defined by pseudo-holomorphic curves.

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